The Roll of Dices in Cryptology

Probability plays a fundamental role in complexity theory, which in turn is one of the pillars of modern cryptology. However, security practitioners are not always familiar with probability theory, and thus fail to foresee the impact of (seemingly small) deviations from the theoretical description of a scheme at the implementation level. On the other hand, many cryptographic scenarios involve mutually distrusting parties, which need however to cooperate towards a joint goal. In order to attain assurance of the good behavior of one party, interactive validation methods (also known as interactive proof systems) are employed. Randomness is at the core of such methods, which most oftenwill only provide relative assurance, in the sense that they will establish correctness in a probabilistic way. In this paper we will briefly discuss the role of probability theory within modern cryptology, reviewing probabilistic proof systems as a powerful tool towards efficient protocol design, and provable security, as an invaluable framework for deriving formal security proofs.